Question: Given $ m \angle BOC = 4x + 42$, and $ m \angle AOB = 5x + 30$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {5x + 30} + {4x + 42} = {180}$ Combine like terms: $ 9x + 72 = 180$ Subtract $72$ from both sides: $ 9x = 108$ Divide both sides by $9$ to find $x$ $ x = 12$ Substitute $12$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 4({12}) + 42$ Simplify: $ {m\angle BOC = 48 + 42}$ So ${m\angle BOC = 90}$.